Question

This question is about a discrete probability distri Poisson distribution, the one which in fact mo- bution known as the Poisson distribution. Let r be a discrete random variable that can take the values 0, 1,2,... A quantity r is said to be Poisson distributed if the probability P(x) of obtaining z is tivated Poisson, was connected with the rare event of someone being kicked to death by a horse in the Prussian army. The number of horse-kick deaths of Prussian military person- nel was recorded for each of 10 corps in each of 20 years from 1875-1894 and the following where m is a particular number (which we will show data recorded: in part (b) of this exercise is the mean value of ) (a) Show that P( is a well-behaved probability Number of deaths per year, per corps Observed distribution in the sense that frequency Pr)- 0 109 65 3 0 (Why is this condition important?) (b) Show that the mean value of the probability distribution is 〈r) = Σ2P(z)-m > 5 c) The Poisson distribution is useful for describ- ing very rare events, which occur indepen dently and whose average rate does not change over the period of interest. Examples include birth defects measured dents at a particular junction per year, num bers of typographical errors on a page, and year per corps the number of activations of a Geiger counter quency with a calculated frequency assuming per minute. The first recorded example of a the number of deaths per year per corps are Total 200 per year, traffic acci Calculate the mean number of deaths per . Compare the observed fre- Poisson distributed with this mean

Answer 1